Derivative and functional graph

Hello, everyone, I encountered a tough problem, urging help. Many thanks. A curve, unknown its functional expression, with approximate 20 extreme points (including min and max), now know the first 10 extreme points (a1…a10) and f(a1-a10), monotony (first 10 points) is clear as well ,is it possible to work out either the rest extreme points or f(a),or both? Thanks.